## Studying at the University of Verona

Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.

## Academic calendar

The academic calendar shows the deadlines and scheduled events that are relevant to students, teaching and technical-administrative staff of the University. Public holidays and University closures are also indicated. The academic year normally begins on 1 October each year and ends on 30 September of the following year.

## Course calendar

The Academic Calendar sets out the degree programme lecture and exam timetables, as well as the relevant university closure dates..

Period | From | To |
---|---|---|

I - II semestre | Oct 2, 2017 | Jun 15, 2018 |

I sem. | Oct 2, 2017 | Jan 31, 2018 |

II sem. | Mar 1, 2018 | Jun 15, 2018 |

Session | From | To |
---|---|---|

Sessione invernale d'esami | Feb 1, 2018 | Feb 28, 2018 |

Sessione estiva d'esame | Jun 18, 2018 | Jul 31, 2018 |

Sessione autunnale d'esame | Sep 3, 2018 | Sep 28, 2018 |

Session | From | To |
---|---|---|

Sessione di laurea estiva | Jul 23, 2018 | Jul 23, 2018 |

Sessione di laurea autunnale | Oct 17, 2018 | Oct 17, 2018 |

Sessione autunnale di laurea | Nov 23, 2018 | Nov 23, 2018 |

Sessione di laurea invernale | Mar 22, 2019 | Mar 22, 2019 |

Period | From | To |
---|---|---|

Christmas break | Dec 22, 2017 | Jan 7, 2018 |

Easter break | Mar 30, 2018 | Apr 3, 2018 |

Patron Saint Day | May 21, 2018 | May 21, 2018 |

VACANZE ESTIVE | Aug 6, 2018 | Aug 19, 2018 |

## Exam calendar

Exam dates and rounds are managed by the relevant Science and Engineering Teaching and Student Services Unit.

To view all the exam sessions available, please use the Exam dashboard on ESSE3.

If you forgot your login details or have problems logging in, please contact the relevant IT HelpDesk, or check the login details recovery web page.

## Academic staff

Magazzini Laura

laura.magazzini@univr.it 045 8028525## Study Plan

The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.**Please select your Study Plan based on your enrollment year.**

1° Year

Modules | Credits | TAF | SSD |
---|

2° Year activated in the A.Y. 2018/2019

Modules | Credits | TAF | SSD |
---|

3° Year activated in the A.Y. 2019/2020

Modules | Credits | TAF | SSD |
---|

Modules | Credits | TAF | SSD |
---|

Modules | Credits | TAF | SSD |
---|

Modules | Credits | TAF | SSD |
---|

Modules | Credits | TAF | SSD |
---|

#### Legend | Type of training activity (TTA)

TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.

### Stochastic systems (2019/2020)

Teaching code

4S00254

Academic staff

Coordinator

Credits

6

Language

Italian

Scientific Disciplinary Sector (SSD)

MAT/06 - PROBABILITY AND STATISTICS

Period

I semestre dal Oct 1, 2019 al Jan 31, 2020.

## Learning outcomes

Stochastic Systems [ Applied Mathematics ]

AA 2018/2019

The Stochastic Systems course aims at giving an introduction to the basic concepts underlying the rigorous mathematical description of the temporal dynamics for random quantities.

The course prerequisites are those of a standard course in Probability, for Mathematics / Physics.

It is supposed that students are familiar with the basics Probability calculus, in the Kolmogorov assiomatisation setting, in particular with respect to the concepts of density function, probability distribution, conditional probability, conditional expectation for random variables, measure theory (basic ), characteristic functions of random variables, convrgence theorems (in measure, almost everywhere, etc.), central limit theorem and its (basic) applications, etc.

The Stochastic Systems course aims, in particular, to provide the basic concepts of: Filtered probability space, martingale processes, stopping times, Doob theorems, theory of Markov chains in discrete and continuous time (classification of states, invariant and limit,measures, ergodic theorems, etc.), basics on queues theory and an introduction to Brownian motion.

A part of the course is devoted to the computer implementation of operational concepts underlying the discussion of stochastic systems of the Markov chain type, both in discrete and continuous time.

A part of the course is dedicated to the introduction and the operational study, via computer simulations, to univariate time series.

It is important to emphasize how the Stochastic Systems course is organized in such a way that students can concretely complete and further develop their own:

° capacity of analysis, synthesis and abstraction;

° specific computational and computer skills;

° ability to understand texts, even advanced, of Mathematics in general and Applied Mathematics in particular;

• ability to develop mathematical models for physical and natural sciences, while being able to analyze its limits and actual applicability, even from a computational point of view;

° skills concerning how to develop mathematical and statistical models for the economy and financial markets;

° capacity to extract qualitative information from quantitative data;

° knowledge of programming languages or specific software.

## Program

Stochastic Systems [ Applied Mathematics ]

AA 2018/2019 Syllabus

1) Markov chains with discrete time and finite state space: irreducibility and aperiodicity, stationary distributions, classification of states, MCMC.

2) Markov chains with countable state space: recurrence, positivity.

3) The Poisson process and other counting processes. Introduction to queuing theory.

4) Markov chains with finite state space and continuous time: associated semigroup, generator, stationary distributions, Kolmogorov equations, rate of convergence to equilibrium and functional inequalities,

Author | Title | Publishing house | Year | ISBN | Notes |
---|---|---|---|---|---|

Levin, David A., and Yuval Peres | Markov chains and mixing times | American Mathematical Society | 2017 | Scaricabile alla pagina https://s3.amazonaws.com/academia.edu.documents/30694248/recent.pdf?response-content-disposition=inline%3B%20filename%3DMarkov_chains_and_mixing_times.pdf&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAIWOWYYGZ2Y53UL3A%2F20191005%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20191005T133241Z&X-Amz-Expires=3600&X-Amz-SignedHeaders=host&X-Amz-Signature=3c046ef319a0d4eaa4a83f4138d7950cb982f2f0c351b6f2e135234f11790559 |

## Examination Methods

Stochastic Systems [ Applied Mathematics ]

AA 2018/2019

The course is diveded into the following three parts

1) Theory of stochastic systems

2) Introduction to time-series analysis

3) Computer exercises ( mainly based on the theory of Markov Chains, in discrete as well in continuous time )

Part (2) will be mainly performed in laboratory mode, using computer equipped classrooms, with the possibility, for each student to use a computer in order to implement , real time, the models proposed during the lesson. This activity will be supported by a tutor for a total amount of 24 (frontal) hours.

Part (3) will be taught by Prof. Caliari in a computer equipped laboratory.

The exam will be subdivided into the following three parts

* a written exam concerning point (1)

* a project presented in agreement with the programme developed with prof. Marco Caliari (point 3)

* exercises and a project concerning point (2)

The programme concerning the written exam, with respect to point (1), is the one reported in the Program section.

The project to be presented with prof. Caliari has to be decided with him.

The project to be presented with respect to point (2), will be chosen, by each student, within the the following list

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

@Projects

@

@Warning: Since the list of projects may vary during the year, Students are warmly invited to directly contact prof. Di @Persio in order to choose the right project to develop, within the list of arguments that will be actually developed @during laboratory hours

@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@

1-Compare the following methods of estimate and/or elimination of time series trends

*First order differences study

*Smoothing with moving average filter

*Fourier transform

*Exponential Smoothing

*Polynomial Data fitting

2- Describe and provide a numerical implementation of the one-step predictor for the following models

FIR(4)

ARX(3,1)

OE(3,1)

ARMA(2,3)

ARMAX(2,1,2)

Box-Jenkins(nb,nc,nd,nf)

3- Compare the Prediction Error Minimization (PEM) and the Maximum Likelihood (ML) approach for the identification of the model parameters (it requires a personal effort in the homes ML)

4- Provide a concrete implementation for the k-fold cross-validation, e.g. using Matlab/Octave, following the example-test that has been given during the lessons

5-Detailed explanation of (at least) one of the following test

*Shapiro-Wilk

*Kolmogorov-Smirnov

*Lilliefors

Practical implementation of the project chosen by the student can be realized exploiting one of the following software frameworks : R, Python, Matlab, Gnu Octave, Excel

The final grade, expressed in thirtieths, will result from the following formula

Rating = (5/6) * T + (1/6) * E + P

where

T is the mark out of 30 on the part of Theory (written exam with prof. Di Persio)

It is the mark out of 30 on the part of Exercises (oral exam with prof. Caliari)

P is a score within the range [0,2]

It is important to emphasize how the objectives of the exam are also centered on assessing the individual student's ability to:

° carry out technical tasks defined in the model-mathematical settings;

° extract qualitative information from quantitative data with particular reference to the analysis of historical series, the study and the realization of predictive models, the development of automatic processes in the analysis of random phenomena;

° use computer/software tools such as R, Matlab, Gnu Octave, etc. , to realize models analyzed in the course and / or implemented in laboratory hours.

**Students with disabilities or specific learning disorders (SLD), who intend to request the adaptation of the exam, must follow the instructions given HERE**

## Type D and Type F activities

**Modules not yet included**

## Career prospects

## Module/Programme news

##### News for students

There you will find information, resources and services useful during your time at the University (Student’s exam record, your study plan on ESSE3, Distance Learning courses, university email account, office forms, administrative procedures, etc.). You can log into MyUnivr with your GIA login details: only in this way will you be able to receive notification of all the notices from your teachers and your secretariat via email and also via the Univr app.

## Graduation

## Documents

Title | Info File |
---|---|

1. Come scrivere una tesi | pdf, it, 31 KB, 29/07/21 |

2. How to write a thesis | pdf, it, 31 KB, 29/07/21 |

5. Regolamento tesi | pdf, it, 171 KB, 20/03/24 |

## List of thesis proposals

theses proposals | Research area |
---|---|

Formule di rappresentazione per gradienti generalizzati | Mathematics - Analysis |

Formule di rappresentazione per gradienti generalizzati | Mathematics - Mathematics |

Proposte Tesi A. Gnoatto | Various topics |

Mathematics Bachelor and Master thesis titles | Various topics |

THESIS_1: Sensors and Actuators for Applications in Micro-Robotics and Robotic Surgery | Various topics |

THESIS_2: Force Feedback and Haptics in the Da Vinci Robot: study, analysis, and future perspectives | Various topics |

THESIS_3: Cable-Driven Systems in the Da Vinci Robotic Tools: study, analysis and optimization | Various topics |

## Attendance modes and venues

As stated in the Teaching Regulations , except for specific practical or lab activities, attendance is not mandatory. Regarding these activities, please see the web page of each module for information on the number of hours that must be attended on-site.

Part-time enrolment is permitted. Find out more on the Part-time enrolment possibilities page.

The course's teaching activities take place in the Science and Engineering area, which consists of the buildings of Ca‘ Vignal 1, Ca’ Vignal 2, Ca' Vignal 3 and Piramide, located in the Borgo Roma campus.

Lectures are held in the classrooms of Ca‘ Vignal 1, Ca’ Vignal 2 and Ca' Vignal 3, while practical exercises take place in the teaching laboratories dedicated to the various activities.

## Career management

## Student login and resources

## Erasmus+ and other experiences abroad

## Ongoing orientation for students

The committee has the task of guiding the students throughout their studies, guiding them in their choice of educational pathways, making them active participants in the educational process and helping to overcome any individual difficulties.

It is composed of professors Lidia Angeleri, Sisto Baldo, Marco Caliari, Paolo dai Pra, Francesca Mantese, and Nicola Sansonetto

To send an email to professors: name.surname@univr.it